High-frequency digital, mixed signal and radio frequency (RF) integrated circuit (IC) design may demand accurate full-wave analyses for pre-layout design optimization and post-layout performance verification. However, full-wave modeling techniques may suffer from large memory requirements and long processor run time. Although algorithms have been studied to mitigate this problem, an integral equation solver may still need O(NlogN) operations and O(NlogN) storage to deal with N-unknown problems; a partial-differential-equation based solver may scale as O(N) in both memory requirement and processor cost. This performance may be regarded as a limit that one can achieve in computational electromagnetics. Since N may be an extremely large number in large-scale IC analysis, the performance of existing full-wave modeling techniques may not be sufficient for realistic high frequency IC design.
The problem may be solved by full-wave modeling and simulation techniques that have limited capacity. For example, commercial tools may be provided within a full-wave-based computer aided design (CAD) market. One tool may be a surface-based integral equation solver. However, its use may be restricted to component design as its computation may be very expensive when the number of surface unknowns exceeds a few thousand. Another tool may be a finite-element-based solver that conducts volumetric discretization. Although the resultant matrix may be sparse, the solution may become difficult if a large number of volume unknowns are involved. The limited capability may prevent the use of existing full-wave techniques in large-scale IC analysis such as pre-layout design of global circuitry and post-layout performance verification. As a result, designers may have to rely on empirical, less-accurate, or inefficient methods in high-frequency digital, mixed signal and RF IC design.